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Why doesn't water fall out of a bucket?

Updated: 9/15/2023
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13y ago

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I assume you mean when the bucket is spinning, so I will answer as such:

If a bucket spins at a sufficient speed, with a sufficient radius, then it will generate a centrifugal force (in reality there is no such thing, but mathematically we can use it to describe the force acting on the bucket and its contents) strong enough to overcome gravity.

Centrifugal force is described as follows:

Fc = mv^2/r

where Fc is the force pushing the water inside of the bucket, m is the mass of the water (that's the only thing we care about right now--I'll explain why later), v is the velocity, and r is the radius you're swinging the bucket about.

Now, the water won't fall out if and only if...

Fc ≥ Fg

where Fg = the force of gravity trying to pull it out of the bucket.

So really, we'd have...

mv^2/r ≥ (9.8)(m)

And here's why the mass doesn't matter: it cancels out! Simplify the equation on both ends to reach:

v^2/r ≥ 9.8

now, 9.8 is an ACCELERATION: it's 9.8m/s^2

To find out whether or not the water falls out of the bucket, fill in the velocity (tangential, not angular: that is, if you "let the bucket go" at any point, v= the speed it would fly away from you) and the radius you're spinning it about. If, when you perform this operation, you result in a number larger than 9.8 meters per second squared, the water stays in the bucket!

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Q: Why doesn't water fall out of a bucket?
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